ocaml: valid sudoku

Author: PoorlyDefinedBehaviour

ocaml/valid_sudoku_dec_08_2023/main.ml

@@ -0,0 +1,178 @@
+(*
+Determine if a 9 x 9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:
+
+Each row must contain the digits 1-9 without repetition.
+Each column must contain the digits 1-9 without repetition.
+Each of the nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition.
+Note:
+
+A Sudoku board (partially filled) could be valid but is not necessarily solvable.
+Only the filled cells need to be validated according to the mentioned rules.
+
+Example 1:
+
+Input: board = 
+[["5","3",".",".","7",".",".",".","."]
+,["6",".",".","1","9","5",".",".","."]
+,[".","9","8",".",".",".",".","6","."]
+,["8",".",".",".","6",".",".",".","3"]
+,["4",".",".","8",".","3",".",".","1"]
+,["7",".",".",".","2",".",".",".","6"]
+,[".","6",".",".",".",".","2","8","."]
+,[".",".",".","4","1","9",".",".","5"]
+,[".",".",".",".","8",".",".","7","9"]]
+Output: true
+Example 2:
+
+Input: board = 
+[["8","3",".",".","7",".",".",".","."]
+,["6",".",".","1","9","5",".",".","."]
+,[".","9","8",".",".",".",".","6","."]
+,["8",".",".",".","6",".",".",".","3"]
+,["4",".",".","8",".","3",".",".","1"]
+,["7",".",".",".","2",".",".",".","6"]
+,[".","6",".",".",".",".","2","8","."]
+,[".",".",".","4","1","9",".",".","5"]
+,[".",".",".",".","8",".",".","7","9"]]
+Output: false
+Explanation: Same as Example 1, except with the 5 in the top left corner being modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.
+ 
+Constraints:
+
+board.length == 9
+board[i].length == 9
+board[i][j] is a digit 1-9 or '.'.
+*)
+
+let char_to_int (c : char) : int =
+  match c with
+  | '1' -> 1
+  | '2' -> 2
+  | '3' -> 3
+  | '4' -> 4
+  | '5' -> 5
+  | '6' -> 6
+  | '7' -> 7
+  | '8' -> 8
+  | '9' -> 9
+  | _ -> assert false
+
+(*
+time O(n)
+space O(1)
+*)
+let is_valid_sudoku (board : char array array) : bool =
+  assert (Array.length board = Array.length board.(0));
+
+  let board_size = Array.length board in
+
+  let valid = ref true in
+
+  let row_or_column = ref 0 in
+
+  (* Check for duplicated numbers in 3x3 grid *)
+  let grid_size = 3 in
+
+  let grid_row_starts_at = ref 0 in
+
+  let grid_column_starts_at = ref 0 in
+
+  (* time O(n) *)
+  while !valid && !grid_row_starts_at <= 6 do
+    while !valid && !grid_column_starts_at <= 6 do
+      let count = Array.make 9 0 in
+
+      for i = 0 to 2 do
+        for j = 0 to 2 do
+          let value =
+            board.(!grid_row_starts_at + i).(!grid_column_starts_at + j)
+          in
+          if value != '.' then (
+            let index = char_to_int value - 1 in
+            count.(index) <- count.(index) + 1;
+
+            if count.(index) > 1 then valid := false)
+        done
+      done;
+
+      grid_column_starts_at := !grid_column_starts_at + grid_size
+    done;
+
+    grid_row_starts_at := !grid_row_starts_at + grid_size;
+    grid_column_starts_at := 0
+  done;
+
+  (* time O(n) *)
+  while !valid && !row_or_column < board_size do
+    (* Check for duplicated numbers in the current row *)
+    let count = Array.make 9 0 in
+
+    for i = 0 to board_size - 1 do
+      (* A value from 1 to 9. *)
+      let value = board.(!row_or_column).(i) in
+      if value != '.' then (
+        let index = char_to_int value - 1 in
+        count.(index) <- count.(index) + 1;
+        if count.(index) > 1 then valid := false)
+    done;
+
+    (* Check for duplicated numbers in the current column *)
+    let count = Array.make 9 0 in
+
+    (* time O(n) *)
+    for i = 0 to board_size - 1 do
+      (* A value from 1 to 9. *)
+      let value = board.(i).(!row_or_column) in
+      if value != '.' then (
+        let index = char_to_int value - 1 in
+        count.(index) <- count.(index) + 1;
+        if count.(index) > 1 then valid := false)
+    done;
+
+    row_or_column := !row_or_column + 1
+  done;
+
+  !valid
+
+let () =
+  Printf.printf "example 1: should be true %b\n"
+    (is_valid_sudoku
+       [|
+         [| '5'; '3'; '.'; '.'; '7'; '.'; '.'; '.'; '.' |];
+         [| '6'; '.'; '.'; '1'; '9'; '5'; '.'; '.'; '.' |];
+         [| '.'; '9'; '8'; '.'; '.'; '.'; '.'; '6'; '.' |];
+         [| '8'; '.'; '.'; '.'; '6'; '.'; '.'; '.'; '3' |];
+         [| '4'; '.'; '.'; '8'; '.'; '3'; '.'; '.'; '1' |];
+         [| '7'; '.'; '.'; '.'; '2'; '.'; '.'; '.'; '6' |];
+         [| '.'; '6'; '.'; '.'; '.'; '.'; '2'; '8'; '.' |];
+         [| '.'; '.'; '.'; '4'; '1'; '9'; '.'; '.'; '5' |];
+         [| '.'; '.'; '.'; '.'; '8'; '.'; '.'; '7'; '9' |];
+       |]);
+
+  Printf.printf "example 2: should be false %b\n"
+    (is_valid_sudoku
+       [|
+         [| '8'; '3'; '.'; '.'; '7'; '.'; '.'; '.'; '.' |];
+         [| '6'; '.'; '.'; '1'; '9'; '5'; '.'; '.'; '.' |];
+         [| '.'; '9'; '8'; '.'; '.'; '.'; '.'; '6'; '.' |];
+         [| '8'; '.'; '.'; '.'; '6'; '.'; '.'; '.'; '3' |];
+         [| '4'; '.'; '.'; '8'; '.'; '3'; '.'; '.'; '1' |];
+         [| '7'; '.'; '.'; '.'; '2'; '.'; '.'; '.'; '6' |];
+         [| '.'; '6'; '.'; '.'; '.'; '.'; '2'; '8'; '.' |];
+         [| '.'; '.'; '.'; '4'; '1'; '9'; '.'; '.'; '5' |];
+         [| '.'; '.'; '.'; '.'; '8'; '.'; '.'; '7'; '9' |];
+       |]);
+
+  Printf.printf "example 3: should be false %b\n"
+    (is_valid_sudoku
+       [|
+         [| '5'; '3'; '.'; '.'; '7'; '.'; '.'; '.'; '.' |];
+         [| '6'; '.'; '.'; '1'; '9'; '5'; '.'; '.'; '.' |];
+         [| '.'; '9'; '8'; '.'; '.'; '.'; '.'; '6'; '.' |];
+         [| '8'; '.'; '.'; '.'; '6'; '2'; '.'; '.'; '3' |];
+         [| '4'; '.'; '.'; '.'; '.'; '3'; '.'; '.'; '1' |];
+         [| '7'; '8'; '.'; '.'; '2'; '.'; '.'; '.'; '6' |];
+         [| '.'; '6'; '.'; '.'; '.'; '.'; '2'; '8'; '.' |];
+         [| '.'; '.'; '.'; '4'; '1'; '9'; '.'; '.'; '5' |];
+         [| '.'; '.'; '.'; '.'; '8'; '.'; '.'; '7'; '9' |];
+       |])